Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×Q64 | C2 | semidirect |
| 2. #71500 | C2 | semidirect |
| 3. C2×#4521 | C2 | semidirect |
| 5. Dic3×C32 | C2 | semidirect |
| 17. C2×Q64 | D3 | semidirect |
| 127. C3 | #13728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q64 | 2 |
| #71500 | 2 |
| C2×#4521 | 2 |
| C2×D96 | 2 |
| Dic3×C32 | 2 |
| #13728 | 3 |